But despite GE’s efforts to control the message in its spat with Connecticut over corporate taxes, people behind the scenes say the company’s ego has been bruised and that could hasten GE’s exit from the state.

When the majority leader of the state House, Joe Aresimowicz, attempted to bring levity to raising taxes on the rich back in June, the Berlin Democrat’s rhetoric struck a nerve at GE, Hearst Connecticut Media has learned.

“I guess the difference between a weekend on the yacht and a regular trip to the grocery store — they can take a weekend off from the yacht,” Aresimowicz said at the time.

While the comments were not directed at the Fairfield-based company or its executives, some interpreted them as a swipe at GE. And they haven’t forgotten.

“These comments are a sign that state leaders are out of touch with the realities of Connecticut’s business climate,” said Seth Martin, a GE spokesman. “As we’ve said before, other states offer more opportunities and a better environment for business growth.”

Aresimowicz, a union ally who represents a blue-collar district, declined to comment Friday.

On the blog of Don Pesci, a conservative commentator on state politics, the newspaper columnist offered a different slant on Aresimowicz’s remarks.

“Mr. Aresimowicz might as easily have said, ‘Let Jeffrey Immelt, the CEO of General Electric, eat his yacht,’ ” Pesci wrote in June.

Lawmakers resorted to raising taxes by $1.2 billion over the next two years to close a billion-dollar budget deficit, targeting the increases at the wealthy and large corporations.

The situation went from bad to worse when the state used a stock image of a jet engine built by in-state rival Pratt & Whitney last month in a PowerPoint presentation to GE. GE brass are still apoplectic over how such an oversight could happen, Hearst Connecticut Media has learned.

GE is expected to decide by the end of the year whether to leave its Fairfield headquarters of 40 years for another state. The company has been smarting over a reduction to a tax break for net operating losses and a looming requirement that it itemize all of its business activity tied to Connecticut.

A dozen other states are pitted in a bidding war for the company’s headquarters, including Rhode Island, which has not received a lot of attention as a potential landing spot but was said by at least one person familiar with the relocation talks to have made a positive impression on GE.

The office of Rhode Island Gov. Gina Raimondo, a Democrat, did not respond Friday to a request for comment.